If you want the same index to have data from both subdomains, then yes, we can add the subdomain to the same application. You will need to contact Support for this request.
If you don't want the same index to have data from both subdomains, then you will need to apply for a separate DocSearch application for the additional subdomain.
The free DocSearch plan, doesn't include technical web support from the Support team. For further assistance, you can post your question on the Algolia Community Forum or Discord. For front-end issues, you can raise the issue directly on GitHub. In addition, you can review our DocSearch Documentation and FAQ.